Dissipative Quantum and Classical Liouville Mechanics of the Anharmonic Oscillator

We present a solution for the dynamics of an anharmonic oscillator coupled to a zero-temperature heat bath. Comparison of observable properties in a classical and quantum description uses true joint phase-space probability densities. The time evolution of the density in the quantum case is rapidly "reduced" to that given in the classical description. The rate of reduction is proportional to the product of the damping rate and the oscillator's initial energy. Quite rapidly, typical quantum recurrence effects are destroyed and the classical "whorl" structure restored. We point out the close similarity with rapid destruction of quantum coherence through dissipation.